Question 201486


{{{(n+5)^2}}} Start with the given expression.



{{{(n+5)(n+5)}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(n)+5)(highlight(n)+5)}}} Multiply the <font color="red">F</font>irst terms:{{{(n)*(n)=n^2}}}.



{{{(highlight(n)+5)(n+highlight(5))}}} Multiply the <font color="red">O</font>uter terms:{{{(n)*(5)=5*n}}}.



{{{(n+highlight(5))(highlight(n)+5)}}} Multiply the <font color="red">I</font>nner terms:{{{(5)*(n)=5*n}}}.



{{{(n+highlight(5))(n+highlight(5))}}} Multiply the <font color="red">L</font>ast terms:{{{(5)*(5)=25}}}.



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So we have the terms: {{{n^2}}}, {{{5*n}}}, {{{5*n}}}, {{{25}}} 



{{{n^2+5*n+5*n+25}}} Now add every term listed above to make a single expression.



{{{n^2+10*n+25}}} Now combine like terms.



So {{{(n+5)^2}}} FOILs to {{{n^2+10*n+25}}}.



In other words, {{{(n+5)^2=n^2+10*n+25}}}.